Observing it later, then much later, gave more visual path lines which all had to properly intersect the asteroid's true orbit path. But just roughly estimating some orbit path wasn't quite good enough. That wouldn't tell how far away, nor how an asteroid orbit's sighting lines tilts might be angled soon toward or away from recent viewing directions. That would require spotting it again and again over months to keep better estimating the orbit distances and speeds and tilt angles.
Gravitational orbit acceleration pulled in by Sol's huge mass determined how the orbit distance out from Sol and the elliptic orbit angle and speed there should all be related. Its viewed passage direction had shown it was orbiting in the same direction around Sol as the planets and other asteroids. (If (extremely unlikely) not, that would've at once been noticed.)
Projecting the successive visual path lines out from the successive viewing positions of the telescope gave more lines in space, which all had to intersect successive orbit positions of the asteroid while in its actual elliptic orbit around Sol. And the orbit intersection points had to be sensibly spaced apart to fit the asteroid's likely orbit speeds then, and distances. The telescope's computer thus kept improving its prior orbit estimates till computing an orbit ever more improved to very closely properly intersect, at proper times and viewing angles, the slowly increasing number of visual path lines.
The computed orbit path had thus gradually kept getting ever finer improved over many months. During all this time, the telescope had much free time to also usefully watch for other possibly (truly) unknown asteroids. This trial test was finally allowed to finish after the telescope's computer had done quite well estimating the asteroid's elliptic orbit and distance from Sol, also its orbit angles away from just a simple circle in the planetary disk. The thus ever better refined asteroid's new computed elliptic orbit ended up nicely matching its previously known orbit. Success!
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